{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Random Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ensemble Averages\n",
    "\n",
    "Ensemble averages characterize the average properties of a random process across the population of all possible sample functions in the ensemble. We distinguish between first- and higher-order ensemble averages. The former consider the average properties of the sample functions of one random process for one particular time-instant $k$, while the latter take more than one random process at different time-instants into account."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First-Order Ensemble Averages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Definition\n",
    "\n",
    "The first-order ensemble average of a continuous-amplitude real-valued random signal $x[k]$ is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ f(x[k]) \\} = \\lim_{N \\to \\infty} \\frac{1}{N} \\sum_{n=0}^{N-1} f(x_n[k]),\n",
    "\\end{equation}\n",
    "\n",
    "where $E\\{ \\cdot \\}$ denotes the expectation operator, $x_n[k]$ the $n$-th sample function and $f(\\cdot)$ an arbitrary real-valued function. It is evident from the definition, that the ensemble average can only be given exactly for random processes where the internal structure is known. For practical random processes, like e.g. speech, the ensemble average can only be approximated by a finite but sufficiently large number $N$ of sample functions.\n",
    "\n",
    "On the other hand, if the univariate probability density function (PDF) which characterizes the process is known, then the ensemble average may also be given as \n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ f(x[k]) \\} = \\int\\limits_{-\\infty}^{\\infty} f(\\theta) \\, p_x(\\theta, k) \\, \\mathrm{d}\\theta.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Properties\n",
    "\n",
    "The following properties can be concluded from the definition of the ensemble average:\n",
    "\n",
    "1. The ensemble averages of two different time-instants $k_1$ and $k_2$ generally differ\n",
    "\n",
    "    \\begin{equation}\n",
    "    E\\{ f(x[k_1]) \\} \\neq E\\{ f(x[k_2]) \\}\n",
    "    \\end{equation}\n",
    "    \n",
    "2. For a linear mapping $f(x[k]) = C \\cdot x[k]$ with $C \\in \\mathbb{R} \\setminus \\{0\\}$, the ensemble average is a linear operation\n",
    "    \n",
    "    \\begin{equation}\n",
    "    E\\{ A \\cdot x[k] + B \\cdot y[k] \\} = A \\cdot E\\{ x[k] \\} + B \\cdot E\\{ y[k] \\}\n",
    "    \\end{equation}\n",
    "\n",
    "3. For a deterministic signal $x_n[k] = s[k]$ $\\forall n$ the ensemble average is \n",
    "\n",
    "    \\begin{equation}\n",
    "    E\\{ f(s[k]) \\} = f(s[k])\n",
    "    \\end{equation}\n",
    "\n",
    "The choice of the mapping function $f(\\cdot)$ determines the particular property of the random process which is characterized by the ensemble average. Common and in practice most important choices are discussed in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear mean (1st raw moment)\n",
    "\n",
    "The linear [mean](https://en.wikipedia.org/wiki/Mean), which is given for the linear mapping $f(x[k]) = x[k]$ is the arithmetic mean value across all sample functions $x_n[k]$ for a given time instant $k$. It is also known as the first raw [moment](https://en.wikipedia.org/wiki/Moment_%28mathematics%29).\n",
    "\n",
    "Introducing $f(x[k]) = x[k]$ into the definition of the ensemble average yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\mu_x[k] = E\\{ x[k] \\} = \\lim_{N \\to \\infty} \\frac{1}{N} \\sum_{n=0}^{N-1} x_n[k].\n",
    "\\end{equation}\n",
    "\n",
    "If the PDF of the process is known, then the linear mapping $f(\\theta)=\\theta$ yields \n",
    "\n",
    "\\begin{equation}\n",
    "\\mu_x[k] = E\\{ x[k] \\} = \\int\\limits_{-\\infty}^{\\infty} \\theta \\, p_x(\\theta, k) \\, \\mathrm{d}\\theta.\n",
    "\\end{equation}\n",
    "\n",
    "$\\mu_x[k]$ is a widely accepted standard notation for the linear mean. A process with $\\mu_x[k] = 0$ is termed as *zero-mean* or *mean-free*. Note that $\\mu_x$ should not be confused with the discrete frequency index of the DFT."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Quadratic mean (2nd raw moment)\n",
    "\n",
    "The quadratic mean is given by the mappings $f(x[k]) = x^2[k]$ and $f(\\theta)=\\theta^2$. The expectation becomes\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ x^2[k] \\} = \\lim_{N \\to \\infty} \\frac{1}{N} \\sum_{n=0}^{N-1} x_n^2[k]\n",
    "= \\int\\limits_{-\\infty}^{\\infty} \\theta^2 \\, p_x(\\theta, k) \\, \\mathrm{d}\\theta.\n",
    "\\end{equation}\n",
    "\n",
    "It quantifies the average instantaneous power of a sample function for a given time index $k$. It is also known as second raw moment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Variance (2nd central moment)\n",
    "\n",
    "The [variance](https://en.wikipedia.org/wiki/Variance) is defined as the quadratic mean of a zero-mean random process. Note that the subtraction of the linear mean $\\mu_x$ from the samples $x_n[k]$ makes a random signal mean-free. We are free to do this prior to calculation of the expectation. Then, for a general random process with linear mean $\\mu_x$ this is given as\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma_x^2[k] = E\\{ (x[k] - \\mu_x[k])^2 \\} = E\\{ \\left(x[k] - E\\{ x[k] \\}\\right)^2 \\},\n",
    "\\end{equation}\n",
    "\n",
    "where $\\sigma_x^2[k]$ commonly denotes the variance, $\\sigma_x[k]$ is known as the [standard deviation](https://en.wikipedia.org/wiki/Standard_deviation). The variance characterizes how far the amplitude values of a random signal are spread out from its mean value. It is also known as second central moment.\n",
    "\n",
    "The variance can be given in terms of the quadratic mean and the squared linear mean\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma_x^2[k] = E\\{ x^2[k] \\} - \\mu_x^2[k]\n",
    "\\end{equation}\n",
    "\n",
    "or vice versa, the quadratic mean is the sum of the squared linear mean and the variance \n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ x^2[k] \\} = \\mu_x^2[k] + \\sigma_x^2[k].\n",
    "\\end{equation}\n",
    "\n",
    "This dependence has a strong link to power calculation of pure resistor circuits in electrical engineering: The complete signal power is the sum of the powers of the direct component (DC) and the alternating component (AC).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Excercise**\n",
    "\n",
    "* Derive above relation from the definitions and properties of the first order ensemble average.\n",
    "\n",
    "Solution: Taking the linearity of the expectation operator and the fact that the linear mean is a deterministic value into account yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\sigma_x^2[k] &= E\\{ (x[k] - \\mu_x[k])^2 \\} \\\\\n",
    "&= E\\{ x^2[k] - 2 \\mu_x[k] x[k] + \\mu_x^2[k]  \\} \\\\\n",
    "&= E\\{ x^2[k] \\} - 2 \\mu_x[k] E\\{ x[k] \\} + \\mu_x^2[k] \\\\\n",
    "&= E\\{ x^2[k] \\} - 2 \\mu_x[k] \\mu_x[k] + \\mu_x^2[k] \\\\\n",
    "& = E\\{ x^2[k] \\} - \\mu_x^2[k]\n",
    "\\end{split}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Linear and quadratic mean, and variance of a random process\n",
    "\n",
    "The following example computes and plots the linear mean $\\mu_x$ and quadratic mean, and variance $\\sigma_x^2$ of a random process. Since in practice only a limited number $N$ of sample functions can be evaluated numerically the true values of these quantities are only approximated/estimated. Estimated quantities are denoted by a 'hat' over the respective quantity, e.g. $\\hat{\\mu}_x[k]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "(0.0, 64.0, 0.0, 1.5)"
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     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "K = 64  # number of random samples\n",
    "N = 1000  # number of sample functions\n",
    "\n",
    "\n",
    "# generate the sample functions\n",
    "np.random.seed(3)\n",
    "x = np.random.normal(size=(N, K))\n",
    "x += np.tile(np.cos(2 * np.pi / K * np.arange(K)), [N, 1])\n",
    "\n",
    "# estimate the linear mean as ensemble average\n",
    "mu = 1 / N * np.sum(x, 0)\n",
    "# estimate the quadratic mean\n",
    "qu = 1 / N * np.sum(x**2, 0)\n",
    "# estimate the variance\n",
    "sigma = 1 / N * np.sum((x - mu) ** 2, 0)\n",
    "\n",
    "\n",
    "# plot results\n",
    "plt.rc(\"figure\", figsize=(10, 3))\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(x[0, :], basefmt=\"C0:\", linefmt=\"C0-\", markerfmt=\"C0o\", label=r\"$x_0$\")\n",
    "plt.stem(x[1, :], basefmt=\"C1:\", linefmt=\"C1--\", markerfmt=\"C1o\", label=r\"$x_1$\")\n",
    "plt.stem(x[2, :], basefmt=\"C2:\", linefmt=\"C2-.\", markerfmt=\"C2o\", label=r\"$x_2$\")\n",
    "plt.title(r\"Sample functions $x_0[k]$, $x_1[k]$, $x_2[k]$\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$x[k]$\")\n",
    "plt.axis([0, K, -4, 4])\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(mu, basefmt=\"C0:\", linefmt=\"C0-\", markerfmt=\"C0o\", label=r\"$\\hat{\\mu}_x[k]$\")\n",
    "plt.stem(\n",
    "    mu**2, basefmt=\"C1:\", linefmt=\"C1--\", markerfmt=\"C1o\", label=r\"$\\hat{\\mu}^2_x[k]$\"\n",
    ")\n",
    "plt.title(r\"Estimate of linear mean and squared linear mean\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$\\hat{\\mu}_x[k]$, $\\hat{\\mu}^2_x[k]$\")\n",
    "plt.axis([0, K, -1.5, 1.5])\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(qu, basefmt=\"C0:\")\n",
    "plt.title(r\"Estimate of quadratic mean\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$\\hat{E}\\{x^2[k]\\}$\")\n",
    "plt.axis([0, K, 0, 2.5])\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(sigma, basefmt=\"C0:\")\n",
    "plt.title(r\"Estimate of variance\")\n",
    "plt.xlabel(r\"$k$\")\n",
    "plt.ylabel(r\"$\\hat{\\sigma}^2_x[k]$\")\n",
    "plt.axis([0, K, 0, 1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* What does the linear and quadratic mean, and the variance tell you about the average behavior of the sample functions?\n",
    "* Change the number `N` of sample functions and rerun the example. What influence has a decrease/increase of the sample functions on the estimated ensemble averages?\n",
    "\n",
    "Solution: Inspection of the estimated linear mean reveals that in average the sample functions follow a cosine function with respect to the sample index $k$. The variance shows that the amount of which the samples of the sample functions for one particular time-instant $k$ are spread around the linear mean is constant. The estimate of the quadratic mean is given as $\\hat{E}\\{ x^2[k] \\} = \\hat{\\mu}_x^2[k] + \\hat{\\sigma}_x^2[k]$. The higher the number $N$ of sample functions used for the estimate of the ensemble averages, the lower the uncertainty in comparison to the true values becomes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second-Order Ensemble Averages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Definition\n",
    "\n",
    "The second-order ensemble average of two continuous-amplitude, real-valued random signals $x[k]$ and $y[k]$ is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ f(x[k_x], y[k_y]) \\} := \\lim_{N \\to \\infty} \\frac{1}{N} \\sum_{n=0}^{N-1} f(x_n[k_x], y_n[k_y]).\n",
    "\\end{equation}\n",
    "\n",
    "It is given in terms of the bivariate PDF as\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ f(x[k_x], y[k_y]) \\} = \\iint\\limits_{-\\infty}^{\\infty} f(\\theta_x, \\theta_y) \\, p_{xy}(\\theta_x, \\theta_y, k_x, k_y) \\, \\mathrm{d}\\theta_x\\, \\mathrm{d}\\theta_y.\n",
    "\\end{equation}\n",
    "\n",
    "The definition of the second-order ensemble average can be extended straightforward to the case of more than two random variables. The resulting ensemble average is then termed as higher-order ensemble average. \n",
    "\n",
    "By setting $y = x$, the second-order ensemble average can also be used to characterize the average properties of the sample functions between two different time-instants $k_1$ and $k_2$ of one random process\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "E\\{ f(x[k_1], x[k_2]) \\} &= \\lim_{N \\to \\infty} \\frac{1}{N} \\sum_{n=0}^{N-1} f(x_n[k_1], x_n[k_2]) \\\\\n",
    "&= \\iint\\limits_{-\\infty}^{\\infty} f(\\theta_1, \\theta_2) \\, p_{xx}(\\theta_1, \\theta_2, k_1, k_2) \\, \\mathrm{d}\\theta_1\\, \\mathrm{d}\\theta_2.\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "It is worth to note that for $y = x$ and equal time-instant $k$, the first-order ensemble average $E\\{ f(x[k]) \\} = \\int\\limits_{-\\infty}^{\\infty} f(\\theta) \\, p_x(\\theta, k) \\, \\mathrm{d}\\theta$ is obtained. Thus, the definition of the higher-order ensemble average constitutes a general formulation of the expectation $E\\{\\cdot\\}$.\n",
    "\n",
    "The choice of the mapping function $f(\\cdot)$ determines the particular property of the random process which is characterized by the ensemble average. The important case of a linear mapping is discussed in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cross-correlation function\n",
    "\n",
    "The [cross-correlation function](https://en.wikipedia.org/wiki/Cross-correlation) (CCF) of two random signals $x[k]$ and $y[k]$ is defined as the second-order ensemble average for a linear mapping $f(x[k_x], y[k_y]) = x[k_x] \\cdot y[k_y]$\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[k_x, k_y] = E\\{ x[k_x] \\cdot y[k_y] \\}.\n",
    "\\end{equation}\n",
    "\n",
    "It characterizes the statistical dependencies of two random signals $x[k]$ and $y[k]$ at two different time instants $k_x$ and $k_y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Auto-correlation function\n",
    "\n",
    "The [auto-correlation function](https://en.wikipedia.org/wiki/Autocorrelation) (ACF) of a random signal $x[k]$ is defined as the second-order ensemble average for a linear mapping $f(x[k_1], x[k_2]) = x[k_1] \\cdot x[k_2]$\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xx}[k_1, k_2] = E\\{ x[k_1] \\cdot x[k_2] \\}.\n",
    "\\end{equation}\n",
    "\n",
    "It characterizes the average statistical dependencies between the samples of a random signal $x[k]$ at two different time instants $k_1$ and $k_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Auto-correlation function of a random signal\n",
    "\n",
    "The following example estimates the ACF of a random signal $x[k]$ as ensemble average of a finite number $N$ of sample functions. The ACF is plotted as image where the colors denote the level of the ACF $\\varphi_{xx}[k_1, k_2]$ for given time-instants $k_1$ and $k_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 64.0, 0.0, 64.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 64  # number of random samples\n",
    "N = 1000  # number of sample functions\n",
    "\n",
    "# generate sample functions\n",
    "np.random.seed(1)\n",
    "r = np.random.normal(size=(N, L))\n",
    "h = np.random.normal(size=(N, 10))\n",
    "x = np.asarray(\n",
    "    [np.convolve(r[n, :], h[n, :], mode=\"same\") for n in range(N)]\n",
    ") + np.tile(np.cos(2 * np.pi / L * np.arange(L)), [N, 1])\n",
    "\n",
    "# estimate the auto-correlation function (ACF)\n",
    "acf = np.zeros((L, L))\n",
    "for n in range(L):\n",
    "    for m in range(L):\n",
    "        # x[0, n] * x[0, m] is the product of the 0-th sample function at two different time-steps n,m\n",
    "        # the individual products are then summed up for all N sample functions\n",
    "        acf[n, m] = 1 / N * np.sum(x[:, n] * x[:, m], axis=0)\n",
    "\n",
    "\n",
    "# plot ACF\n",
    "plt.figure(figsize=(7, 5))\n",
    "plt.pcolormesh(np.arange(L + 1), np.arange(L + 1), acf)\n",
    "plt.title(r\"Estimate of ACF $\\hat{\\varphi}_{xx}[k_1, k_2]$\")\n",
    "plt.xlabel(r\"$k_1$\")\n",
    "plt.ylabel(r\"$k_2$\")\n",
    "plt.colorbar()\n",
    "plt.axis(\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Can you explain the specific symmetry of the ACF?\n",
    "\n",
    "Solution: Inspection of the definition of the ACF $\\varphi_{xx}[k_1, k_2] = \\lim_{N \\to \\infty} \\frac{1}{N} \\sum_{n=0}^{N-1} x_n[k_1] \\cdot x_n[k_2]$ reveals that the sample indexes $k_1$ and $k_2$ can be interchanged without changing the value of the ACF. Hence, $\\varphi_{xx}[k_1, k_2] = \\varphi_{xx}[k_2, k_1]$. This symmetry can be observed in above plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
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 },
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}
